I strongly disagree that Tarasova did anything to improve Mao's skating. Everything went backwards under Tarasova and the programs were dreadful, failing to capitalize on Mao's greatest strength - the otherworldly, etherial aspect of her skating.
I have enormous respect for Tarasova and consider her the greatest coach, if not in the history of the sport, then of the last 30 years. But her reputation has been made working closely with skaters who trained directly under her supervision. She has been less successful when she simply choreographs for skaters she doesn't otherwise work with. When TT works with a skaters as a coach, she gets to know them, their style and their strengths. Then she choreographs to their strengths, minimizes their weaknesses, and builds brilliant programs for them. Without that day to day interaction, she simply imposes her vision on the skaters, with less success.